side of a polygon
segment that forms a polygon
vertex of a polygon
common endpoint of two sides
diagonal
segment that connects any two non consecutive vertices
regular polygon
equilateral and equiangular polygon
concave
any point of a diagonal contains points in the exterior of the polygon
convex
no diagonal contains points in the exterior
Polygon Angle Sum Theorem
The sum of the interior angles of a convex polygon with n sides is (n-2)180 degrees
Polygon Exterior Angle Sum Theorem
The sum of the exterior angle measures, on angle at each vertex, of a convex polygon is 360 degrees
parallelogram
a quadrilateral with two pairs of parallel sides
Theorem 6-2-1
If a quadrilateral is a parallelogram, then its opposite sides are congruent
Theorem 6-2-2
If a quadrilateral is a parallelogram, then the opposite angles are congruent
Theorem 6-2-4
If a quadrilateral is a parallelogram, then its diagonals bisect each other
Theorem 6-2-3
if a quadrilateral is a parallelogram, then its consecutive angles are supplementary
Theorem 6-3-1
If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram
Theorem 6-3-2
If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram
Theorem 6-3-3
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram
Theorem 6-3-4
If an angle of a quadrilateral is supplementary to both of ts consecutive angles, then the quadrilateral is a parallelogram
Theorem 6-3-5
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram
rectangle
a quadrilateral with four right angles
rhombus
a quadrilateral with four congruent sides
square
a quadrilateral with four right angles and four congruent sides
Theorem 6-4-1
If a quadrilateral is a rectangle, then it is a parallelogram
Theorem 6-4-2
If a parallelogram is a rectangle, then its diagonals are congruent
Theorem 6-4-3
If a quadrilateral is a rhombus, then it is a parallelogram
Theorem 6-4-4
If a parallelogram is a rhombus, then's diagonals are perpendicular
Theorem 6-4-5
If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles
Theorem 6-5-1
If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle
Theorem 6-5-2
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle
Theorem 6-5-3
If one pair of consecutive sides of a parallelogram is congruent, then the parallelogram is a rhombus
Theorem 6-5-4
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus
Theorem 6-5-5
If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus
kite
a quadrilateral with exactly two pairs of congruent consecutive sides
trapezoid
a quadrilateral with exactly one pair of parallel sides
base of a trapezoid
each of the parallel sides of a trapezoid
leg of a trapezoid
a non parallel side of a trapezoid
base angle of a trapezoid
two consecutive angles with a common base side of a trapezoid
isosceles trapezoid
the legs of a trapezoid are congruent
midsegment of a trapezoid
a segment whose endpoints are the midpoints of the legs of a trapezoid
Theorem 6-6-1
If a quadrilateral is a kite, then its diagonals are perpendicular
Theorem 6-6-2
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent
Theorem 6-6-3
If a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent
Theorem 6-6-4
If a trapezoid has a pair of congruent base angles, then the trapezoid is isosceles
Theorem 6-6-5
A trapezoid is isosceles if and only if its diagonals are congruent
Trapezoid Midsegment Theorem
The midsegment of a trapezoid is parallel to each base, and its length is half the sum of the bases' lengths